Sure, let's solve for the slope [tex]\( m \)[/tex] in the equation [tex]\( y = mx + b \)[/tex].
Given the equation,
[tex]\[ y = mx + b, \][/tex]
we need to isolate [tex]\( m \)[/tex].
Step 1: Subtract [tex]\( b \)[/tex] from both sides of the equation.
[tex]\[ y - b = mx + b - b \][/tex]
Simplifying, we get:
[tex]\[ y - b = mx \][/tex]
Step 2: Divide both sides by [tex]\( x \)[/tex] to isolate [tex]\( m \)[/tex].
[tex]\[ \frac{y - b}{x} = m \][/tex]
Rewriting this, we get:
[tex]\[ m = \frac{y - b}{x} \][/tex]
So, the equivalent equation solved for the slope [tex]\( m \)[/tex] is:
[tex]\[ m = \frac{y - b}{x} \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{m = \frac{y - b}{x}} \][/tex]
